Non-Gaussian signatures of gravitational lensing in the microwave background

Gravitational lensing by large-scale structure is shown to give non-Gaussian signatures in the cosmic microwave background radiation (CMBR). The distribution function of the CMBR temperature fluctuations exhibits only minuscule effects of gravitational lensing; it is thus a null experiment and if a significant kurtosis were to be observed, it could not have been generated by lensing. Gravitational lensing stretches and compresses the sky while conserving surface brightness. The spatial derivatives are strongly affected by lensing, generating a measurable kurtosis in the distribution functions of the two first derivatives. For a model with Omega(0) = 0.3 and Omega(A) = 0.7 the kurtosis is approximately 0.1 on a scale of 10'. The kurtosis is approximately 0.05 for Omega(0) = 1, Omega(A) = 0. This is measurable with a sample of less than 10' data points. The kurtosis is a maximum likelihood estimate of the amplitude of the lensing and it is very sensitive to Omega(A).